On the attractors of Feigenbaum maps
Tom 110 / 2014
Annales Polonici Mathematici 110 (2014), 55-62 MSC: Primary 37B25; Secondary 54H20. DOI: 10.4064/ap110-1-5
A solution of the Feigenbaum functional equation is called a Feigenbaum map. We investigate the likely limit set (i.e. the maximal attractor in the sense of Milnor) of a non-unimodal Feigenbaum map, prove that it is a minimal set that attracts almost all points, and then estimate its Hausdorff dimension. Finally, for every $s\in (0,1)$, we construct a non-unimodal Feigenbaum map with a likely limit set whose Hausdorff dimension is $s$.